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Cooperative Beamforming and Jammer Selection Strategies for Two-Hop Secure Communication Hao Deng1,2 , Hui-Ming Wang1 , Chaowen Liu1 ,Tong-Xing Zheng1 , and Wenjie Wang1 1
School of Electronic and Information Engineering Xi’an Jiaotong University Xi’an, 710049, Shaanxi, P. R. China Email:
[email protected]
2
School of Physics and Electronics Henan University Kaifeng, 475004, Henan, P. R. China Email:
[email protected]
cooperative beamforming and jamming scheme to enhance the security of a cooperative relay network. Both the schemes proposed in [10] and [11] require that the cooperative nodes coordinate the artificial noise a priori. To deal with these two problems, we propose a joint cooperative beamforming and jammer selection scheme. Both path-loss and small-scale fading are considered in our channel model. We assume that the eavesdropper’s instantaneous CSI is not available. In the first phase, the source broadcasts its information signal, the selected jammer and the destination simultaneously transmit independent jamming signals to confuse the potential eavesdropper, while the other relays keep listening. In the second phase, all the relay nodes transmit a weighted version of the received signal to achieve a maximum SNR at the destination. The jammer selection schemes proposed in [12] are based on the global instantaneous CSI of the legitimate nodes and the eavesdropper. Furthermore, the jamming signals interfere with the destination. While in our scheme, the jammer selection only relies on the secondorder statistics of the channel gains and we guarantee that the jamming signal is cancelled out at the destination.
Abstract—In this paper, we propose a novel scheme to enhance the security of a single source-destination cooperative network with multiple helpers and one eavesdropper, where a helper operates as a jammer and the others use amplify-and-forward (AF) protocol to deliver a weighted version of the received signal. Since the instantaneous channel state information (CSI) of the eavesdropper is not available, we hope to achieve the maximum signal-to-noise ratio (SNR) and guarantee that the jamming signal is cancelled out at the destination. The weights of the relay can be obtained by just solving a semidefinite programming (SDP) without bisection search. We provide two jammer selection strategies for two cases, i.e., with or without knowledge of the eavesdropper’s position. Simulation results confirm a great improvement of the security in the considered network. Keywords-Physical layer security; cooperative jamming; jammer selection; cooperative communications
I. I NTRODUCTION Physical layer security, which can exploit the characteristics of wireless channels for guaranteeing security [1], has received a lot of attention recently [2]-[8]. Typically, the eavesdropper is passive and hence the legitimate nodes have no knowledge of the eavesdropper’s CSI. In such case, secure communication can be guaranteed by selectively degrading the eavesdropper’s channel via friendly jamming. This was first introduced by Goel and Negi in [8]. Differing from [8], the authors in [9] proposed a new way to coordinate the artificial noise/jamming signal between the legitimate nodes. These schemes indeed can enhance security by reducing the signal strength at the eavesdropper. However, the helpers in [8] and [9] only operate as jammers, which gives no benefit to improve the channel quality between the source and the destination. The scheme named opportunistic relay chatting in [10] uses a group of relays to transmit common artificial noise via distributed beamforming and select a best relay to forward information signal. And the authors in [11] proposed a joint
II. S YSTEM M ODEL In this paper, we denote vectors and matrices with bold font. H denotes the Hermitian operator, denotes the elementwise Schur-Hadamard product, and diag(v) denotes a diagonal matrix with diagonal entries consisting of the elements of the vector v. [·]m,n is the (m,n)-th element of a matrix. E(X) denotes the expectation of X and IN is a N × N identity matrix. We consider a wireless cooperative network of one source S, one destination D, and N helpers Ri ∈ R in the presence of one eavesdropper E, for i = 1, · · · , N . All nodes in this network are equipped with a single antenna. Since the eavesdropper is a single antenna node, only one helper is selected as jammer J and the other N − 1 helpers act as relay nodes, as shown in Fig.1. However, our results can extend to more than one jammers case easily. For convenience, we assume that the N -th helper is selected as the jammer. The jammer selection strategies will be given in Section III. The main and wiretap links are represented by solid lines and dash clines respectively, both of them are modeled as − hij = dij 2 gij for i ∈ S, D, J, Ri and j ∈ D, E, Ri , where
The contact author is Hui-Ming Wang. This work was partially supported by the NSFC under Grant No. 61221063, No.61102081, No.61172092, and No.61172093, the Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant 201340, the National High-Tech Research and Development Program of China under Grant No. 2015AA011306, the New Century Excellent Talents Support Fund of China under Grant NCET13-0458, the Fok Ying Tong Education Foundation under Grant 141063, and the Fundamental Research Funds for the Central University under Grant No. 2013jdgz11.
k,(((
dij is the distance between nodes i and j, c is the path-loss exponent(typically between 2 and 6), and gij follows with CN (0, 1). For simplicity, we assume that noises at all the nodes are complex additive white Gaussian noise with zero mean and variance σ 2 .
a is generated by D, D can cancel it by self-interference substraction. Therefore, the received signal at D is equivalently rewritten as (7) yD = Ps wH hSRD s + n ¯D . Then the mutual information at D is given by
R1
hSRi
R2
RN-1
hSE
hRi E hJE
I(yD ; s) = log (1 + ΓD ) Ps wH HSD w , = log 1 + 2 σ (1 + wH HRD w)
hDRi hJRi J
(8)
where I(·; ·) is mutual information, HSD = hSRD hH SRD , and HRD = diag(|hR1 D |2 , · · · , |hRN −1 D |2 ). Combining (2) and (5) yields the receive model of the eavesdropper in the whole procedure as
hDE
y E = h E s + nE ,
Figure 1. System Model.
(9)
where For AF protocol, two phases are needed for one data transmission from S to D. During phase 1, S broadcasts its data, while D and J simultaneously transmit independent jamming signals to mask the information transmission. The signals received at Ri and E are, respectively yRi = Ps hSRi s + Pz hJRi z + Pa hDRi a + nRi , (1) (1) (1) yE = Ps hSE s + Pz hJE z + Pa hDE a + nE , (2)
(1)
Ps [hSE , wH hSRE ]T ,
(10)
√ (1) Pz hJE z + Pa hDE a + nE nE = √ , √ (2) Pz wH hJRE z + Pa wH hDRE a + n ¯E (11) Then the mutual information of the eavesdropper is
√
I(yE ; s) = log |HE + QE | − log |QE | ,
where Ps , Pz and Pa are the transmit powers of the source, the jammer and the destination, respectively, z and a are the (1) jamming signals, nRi and nE are the additive noises. We 2 assume that E{|s| } = E{|z|2 } = E{|a|2 } = 1. During phase 2, the signal transmitted by the relay node Ri is xRi = wi yRi , (3)
(12)
where HE = hE hH E , QE is the covariance matrix of nE which has the following form
q11 q12 , (13) QE = q21 q22 with
where wi is the weight of Ri . Under the individual power constraint, we should have E{|xRi |2 } ≤ PR , for i = 1, 2, · · · , N − 1. The received signals at D and E are yD = Ps wH hSRD s + Pa wH hDRD a+ (4) Pz wH hJRD z + n ¯D , (2) yE = Ps wH hSRE s + Pa wH hDRE a+ (5) (2) Pz wH hJRE z + n ¯E ,
q11 =Pz |hJE |2 + Pa |hDE |2 + σ 2 , q22 =Pz wH HJE w + Pa wH HDE w + σ 2 (wH HRE w + 1), ∗ = Pz hJE wT h∗JRE + Pa hDE wT h∗DRE , q12 =q21 H where HJE = hJRE hH JRE , HDE = hDRE hDRE , HRE = 2 2 diag(|hR1 E | , · · · , |hRN −1 E | ). Based on (9) and (13), the instantaneous secrecy rate of the proposed scheme can be given by
(2)
1 + Rs = (I(yD ; s) − I(yE ; s)) 2 1 + = (log (1 + ΓD ) + log |QE | − log |HE + QE |) , 2 (14) + where (x) = max(0, x). Since the eavesdropper’s instantaneous CSI is unknown, the instantaneous secrecy rate in (14) can not be directly computed. We may not do any optimization to obtain Rs , thus we turn to maximize I(yD ; s) by finding the joint optimal solution of the relay weights and jammer selection.
¯ E = wH (hRE nR ) where n ¯ D = wH (hRD nR ) + nD , n T (2) +nE , hmRn = hmR1 hR1 n , · · · , hmRN −1 hRN −1 n , hRn = T hR1 n , · · · , hRN −1 n , for m ∈ {S, D, J} and n ∈ {D, E}, ∗ T T w = [w1∗ , w2∗ , · · · , wN −1 ] and nR = [nR1 , · · · , nRN −1 ] . Obviously, the jamming signal forwarded by the relays should not interfere with the destination. Thus we have wH hJRD = 0.
(2)
yE = [yE , yE ]T , hE =
(6)
Then the beamformer w should be in the form of w = Fv, where F is the null space of hJRD . Besides, the artificial noise
search [14]. Herein we give an algorithm for beamformer designing t = FH hSRD without bisection search. Let and N −1 Θ = θ = (θ1 , · · · , θN −1 )|θi ≥ 0, ∀i; i=1 θi = 1 . The problem of (18) is equivalent to [15]
III. JAMMER S ELECTION AND O PTIMIZATION In practice, the eavesdropper’s instantaneous CSI or even the statistics of the CSI may be unavailable. However, if the eavesdropper is an unwanted user of the communication system, the large-scale fading coefficients may be tracked. Then the knowledge of the eavesdropper’s position can be obtained. Intuitively, the knowledge of the eavesdropper’s position can bring benefit to enhance security. We herein consider two cases, the case with knowledge of the eavesdropper’s position or without.
max v=0
θ∈Θ
1) Jammer Selection: We start from the instantaneous SNR at D in (8) Ps wH HSD w ΓD = 2 , (15) σ (1 + wH HRD w)
tH v=1
it is worth to noting that ΓD is variant with different selected jammer. Obviously, the optimal jammer selection is needed to train the CSIs of all the main links, including S → Ri → D, J → Ri → D and Ri → D, for i = 1, · · · , N − 1. However the optimal jammer is selected out of the N helpers, the overhead is fairly high for training CSI of the J → Ri → D links with a large number of helpers. To reduce overhead, we consider the problem of jammer selection with the secondorder statistics of the main links to maximize the average SNR at the destination. The approximate average SNR at D is
i=1,i=J
J = arg max J∈R
s.t.
Ps w HSD w (1 + wH HRD w) w = Fv, σ2
(19)
(21)
(22)
The problem of (22) is convex and can be reformulated as min s.t.
d d ≥ 0,
d tH 0, t S
(23)
where the variable is d ∈ R and A 0 denotes that A is a semi-definite matrix. The above problem is a semidefinite program, which can be solved by several high-quality opensource solvers, e.g., SeDuMi and CVX software [16]. Let S∗ denotes the matrix corresponding to the minimum of (22). Then the solution of (18) can be expressed as w∗ =
(17)
κFS−1 ∗ t , tH S−1 ∗ t
(24)
where κ is chosen to satisfy the power constraint. B. With Knowledge of the Eavesdropper’s Position 1) Jammer Selection: In the first phase, the security relies on the jamming level by the selected jammer and the destination. Obviously, the jamming level at the eavesdropper would be high when the selected jammer locates close to the eavesdropper. With knowledge of the eavesdropper’s position, one effect way to degrade the wiretap channel is to select the jammer nearest to the eavesdropper. Therefore the optimal jammer is selected according to
H
w,Ps
S−1 t . tH S−1 t
θ∈Θ
2) Beamformer Optimization: Once the optimal jammer is selected, we want to maximize the SNR at the destination by finding the optimal beamformer. The problem can be formulated as max
,
θ∈Θ tH v=1
Then the problem of (20) is equivalent to min tH S−1 t .
(16)
dSJ .
θ∈Θ
v∗ =
where λmax (A) denotes the largest eigenvalue of A, and J is the index of jammer. The same approximation method has been adopted in [13]. One can easily see that the average SNR at D depends on the distances from the source to the helpers, therefore the optimal jammer is selected according to ∗
+ PR vH Rv
tH v=1
wH E [HSD ] w 1 + wH E [HRD ] w −1 ≤ λmax E [HRD ] E [HSD ] d−c SRi ,
N −1 H H i=1 θi Ti,i v fi fi v
Equation (20) is derived from the minimax theorem. The solution of min vH Sv is given by
¯D = Γ
N
PR |tH v|2
where R = FH HRD F, and fi is the i-th row of F. Since ejϕ v is also a solution for any real number ϕ if v is asolution of (19), we can restrict tH v = 1. Let N −1 H H S = i=1 θi Ti,i fi fi + PR R = F QF + PR R, where Q = diag ([θ1 T1,1 , · · · , θN −1 TN −1,N −1 ]). Then, we reformulate (19) as min max vH Sv = max min vH Sv . (20)
A. Without Knowledge of the Eavesdropper’s Position
=
max
(18)
|wi |2 Ti,i ≤ PR , i = 1, 2, · · · , N − 1, where T = Ps HSR + Pz HJR + Pa HDR + σ 2 IN −1 , HSR = diag(|hSR1 |2 , · · · , |hSRN −1 |2 ), HJR = diag(|hJR1 |2 , · · ·, |hJRN −1 |2 ), and HDR = HRD . Normally the problem in (18) is solved by a SDP relaxation together with a bisection
J ∗ = arg min J∈R
dEJ .
(25)
2) Beamformer Optimization: From (7) and (9), we can see that both the information rate of the destination and the eavesdropper are increasing in Ps . Although the selected jammer and the destination try to prevent the eavesdropper from successfully receiving the information signal, there is still some probability that the eavesdropper has good SNR due to the fact that we can not optimize Ps without the eavesdropper’s CSI. In the first phase, the security relies on the jamming level by the selected jammer and the destination, while in the seconde phase, we already have the other N − 1 relays to interfere with the eavesdropper. So the information leakage may happen mainly in the first phase. Herein we focus on (1) the information leakage in the first phase. Let Γe denotes the SNR at the eavesdropper in thefirst hop and γe denotes (1) a given SNR. We want to make P Γe ≥ γe as small as (1)
possible. Based on (2), Γe
The problem of (29) is equivalent to max v=0
Ps |hSE |2 Pz |hJE |2 + Pa |hDE |2 + σ 2 Ps |hSE |2 ≈ . Pz |hJE |2 + Pa |hDE |2
IV. S IMULATION R ESULTS In this section, we investigate the performance of the proposed transmission schemes numerically. In all the simulations, the path loss c is set to 3.5. The source and the eavesdropper are placed at (0, 0) and (0, 40) , respectively. There are eight helpers placed at (40.6, −4.8), (43.6, −0.4), (56.4, −6.2), (36.3, −16.5), (43.1, −16.7), (35.8, −10.9), (23.0, 17.7) and (42.8, 19.9), respectively. As the destination moves from (70,0) to (100,0) along the horizontal line, the secrecy rates of the system are calculated. The noise power is σn2 = −60dBm, Pa and Pz are limited by 20dBm, and PR is fixed as 10dBm. Note that the eavesdropper locates at a much closer position to the source than that of the destination. Without jamming, the average SNR at the eavesdropper equals to 55dB when Ps = 20dBm. Thus we set β = 0.05, γe = 10dB. Monte Carlo experiments consisting of 1000 independent trials have been performed to obtain the average results.
(26) (27)
2.2
1.8
secrecy rate(nats/s/Hz)
1.6
(28)
The optimization is to find the beamforming vector w and Ps , such that 1) the received SNR at the destination is maximized, and 2) the probability of that the received SNR at the eavesdropper in the first phase keeps above a certain threshold is fairly small. Then, we have max w,Ps
s.t.
Pz γe β(μ2 +μ3 )+
β (μ2 −μ3 )2 +4βμ2 μ3
1
0.6
0.4
0.2 70
(29)
75
80 85 90 X-axis of the destination's position
95
100
In Fig.2, we compare the secrecy rate achieved by our proposed schemes and the schemes in [2]-[3]. Without knowledge of the eavesdropper’s position, Ps is fixed as 20dBm. While with knowledge of the eavesdropper’s position, Ps changes with the position of the destination to satisfy the constraint (1) of P Γe ≥ γe ≤ β. We can see that the secrecy rates of the schemes in [2] and [3] are much lower than ours. This is because our schemes improve the channel quality between the source and the destination, in addition to degrading the wiretap channel by sending jamming signal. Comparing the circle-curve and the triangle-curve, as expected, the knowledge
The last constraint can be further expressed as
1.2
Figure 2. Secrecy rate vs. positions of the destination.
|wi |2 Ti,i ≤ PR , i = 1, 2, · · · , N − 1, ≤ β, ≥ γ P Γ(1) e e
Ps ≤ Psmax , √ 2
1.4
0.8
H
Ps w HSD w σ 2 (1 + wH HRD w) w = Fv,
Jammer selection without position knowledge Jammer selection with position knowledge Yang's scheme[3] Goel's scheme[2]
2
2
μ1 (α) . (μ1 α + μ2 γe )(μ2 α + μ3 γe )
(31)
i
˜ = P max HSR + Pz HJR + Pa HDR + σ 2 IN −1 . where T s With the same proceeding of the problem (19), the optimal beamformer can be easily obtained.
Let X = |hSE |2 , Y = |hJE |2 and Z = |hDE |2 , all of which follow the exponential distribution with μ1 E[X] = d−c SE , −c μ2 E[Y ] = d−c and μ E[Z] = d . Note that only 3 JE DE when the eavesdropper’s position information is available, the values of μ1 , μ2 and μ3 can be obtained. Without loss of generality, we assume that Pz = Pa and Ps = αPz . Then we have P Γ(1) e ≥ γe ∞ ∞ ∞ 1 − ux 1 − uy 1 − ux e 1 dx e 2 dy e 3 dz = Pz (y+z)γe μ μ2 μ3 1 0 0 Ps =
PR |tH v|2 , N −1 ˜ i,i vH f H fi v + PR vH Rv θi T i=1
θ∈Θ
is given by
Γ(1) e =
max
(30)
. As the where Psmax = 2(1−β)μ1 objective function in (29) is increasing in Ps , for any value of w, this objective function is maximized for Ps = Psmax .
of the eavesdropper’s position brings more benefit to secrecy when the destination is not far from the eavesdropper. When the destination gets far from the eavesdropper, the jamming level coming from the destination would decrease.In order to (1) satisfy the probability constraint of P Γe ≥ γe ≤ β, the transmit power of signal should also decrease, and so does the secrecy rate. We can guarantee that the jamming level remains the same via power control, which would be investigated in our future research. We also see that the jammer selection scheme without knowledge of the eavesdropper’s position performs fairly well, indicating that such scheme may be more practical.
[14] V. H. Nassab, S. Shahbazpanahi, A. Grami, and Z. Q. Luo, “Distributed beamforming for relay networks based on second-order statistics of the channel state information,” IEEE Trans. Signal Process., vol. 56, no. 9, pp. 4306-4316, Sep. 2008. [15] J. Li and A. P. Petropulu, “A low complexity algorithm for collabrativerelay beamforming,” in the 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013), Vancouver, BC, Canada, May. 2013. [16] G. Michael and B. Stephen, CVX users guide for CVX ver. 1.21 [Online]. Available: http://cvxr.com/ Apr. 2011
V. C ONCLUSION In this paper, we have proposed a joint cooperative beamforming and jammer selection scheme to enhance the security of a cooperative network. Under the individual power constraint and without instantaneous CSI of the eavesdropper, the beamforming weights are obtained by just solving a SDP problem. Two jammer selection strategies for the case with knowledge of the eavesdropper’s position or without are given. Simulation results show our proposed schemes greatly improve the security. R EFERENCES [1] M. Bloch, J. Barros, M. R. D. Rodriques, and S. W. McLaughlin, “Wireless information-theoretic security,” IEEE Trans. Inf. Theory, vol. 54, pp. 2515-2534, June 2008. [2] L. Dong, Z. Han, A. Petropulu, and H. Poor, “Improving wireless physical layer security via cooperating relays,” IEEE Trans. Signal Process., vol. 58, pp. 1875-1888, Mar. 2010. [3] G. Zheng, L.-C. Choo, and K.-K. Wong, “Optimal cooperative jamming to enhance physical layer security using relays,” IEEE Trans. Signal Process., vol. 59, no. 3, pp. 1317-1322, Mar. 2011. [4] J. Huang and A. L. Swindlehurst, “Cooperative jamming for secure communications in MIMO relay networks,” IEEE Trans. Signal Process., vol. 59, no. 10, pp. 4871-4884, Oct. 2011. [5] H.-M. Wang, Q. Yin, and X.-G. Xia, “Distributed beamforming for physical-layer security of two-way relay networks,” IEEE Trans. Signal Process., vol. 60, no. 7, pp. 3532-3545, Jul. 2012. [6] H.-M. Wang, Miao Luo, Q. Yin, and X.-G. Xia, “Hybrid cooperative beamforming and jamming for physical-layer security of two-way relay networks,” IEEE Trans. Inf. Foren. Sec., vol. 8, no. 12, pp. 2007-2020, Dec. 2013. [7] X. Zhou and M. R. McKay, “Secure transmission with artificial noise over fading channels: achievable rate and optimal power allocation,” IEEE Trans. Veh. Tech., vol. 59, no. 8, pp. 3831-3842, Oct. 2010. [8] S. Goel, R. Negi, “Guaranteeing secrecy using artificial noise,” IEEE Trans. Wireless Commun., vol. 7, no.6, pp. 2180-2189, June 2008. [9] B. Yang, W. Wang, B. Yao, and Q. Yin, “Destination assisted secret wireless communication with cooperative helpers,” IEEE Signal Process. Lett., vol. 20, no.11, pp. 1032-1035, Nov. 2013. [10] Z. Ding, K. Leung, D. L. Goeckel, and D. Towsley, “Opportunistic relaying for secrecy communications: cooperative jamming vs relay chatting,” IEEE Trans. Wireless Commun., vol 10, pp. 1725-1729, June 2011. [11] H.-M. Wang, M. Luo, X.-G. Xia, and Q. Yin, “Joint cooperative beamforming and jamming to secure AF relay systems with individual power constraint and no eavesdroppers CSI,” IEEE Signal Process. Lett., vol. 20, no. 1, pp. 39-42, Jan. 2013. [12] J. Chen, R. Zhang, L. Song, Z. Han, and B. Jiao, “Joint relay and jammer selection for secure two-way relay networks,” IEEE Trans. Inf. Foren. Sec., vol. 7, no. 1, pp. 310-320, Feb. 2012 [13] M. Kobayashi and G. Caire, “Joint beamforming and scheduling for a multi-antenna downlink with imperfect transmitter channel knowledge,” IEEE J. Sel. Areas Commun., vol. 25, no. 7, pp. 1468-1477, Sep. 2007.
